Question

The present age of Geetha is 1/3 of the present age of her mother. After 5 years, sum of their ages will be 46. Form a linear equation in one variable to find the present ages of Geetha and her mother. What are Geetha's and her mother's ages? 

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Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

$\large\underline{\sf{Solution-}}$

Given that

• The present age of Geetha is 1/3 of the present age of her mother.

Let assume that

• Geetha present age be x years.

So,

• Mother present age be 3x years.

Thus, we have

$\red{\begin{gathered}\begin{gathered}\bf\: So-\begin{cases} &\sf{Geetha \: present \: age = x \: years} \\ \\ &\sf{Mother \: present \: age = 3x \: years} \end{cases}\end{gathered}\end{gathered}}$

According to statement

• After 5 years, sum of their ages will be 46.

Thus, After 5 years

$\red{\begin{gathered}\begin{gathered}\bf\: So \: after \: 5 \: yeas-\begin{cases} &\sf{Geetha \: age = x + 5 \: years} \\ \\ &\sf{Mother \: age = 3x + 5\: years} \end{cases}\end{gathered}\end{gathered}}$

$\rm \implies\:x + 5 + 3x + 5 = 46$

$\rm \implies\:4x + 10 = 46$

$\rm \implies\:4x = 46 - 10$

$\rm \implies\:4x = 36$

$\bf \implies\:x = 9$

$\red{\begin{gathered}\begin{gathered}\bf\: So-\begin{cases} &\sf{Geetha \: present \: age = x = 9\: years} \\ \\ &\sf{Mother \: present \: age = 3x = 27 \: years} \end{cases}\end{gathered}\end{gathered}}$

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Basic Concept Used :-

Writing System of Linear Equation from Word Problem.

1. Understand the problem.

• Understand all the words used in stating the problem.

• Understand what you are asked to find.

2. Translate the problem to an equation.

• Assign a variable (or variables) to represent the unknown.

• Clearly state what the variable represents.

3. Carry out the plan and solve the problem.